Mathematical cognition is critical not only for success in science and engineering but also as an important skill in everyday life, second only to reading in formal education. Yet, mathematical difficulties are widespread in school-age children and college students in the US. Understanding the progression and mechanisms of mathematical development is a national priority, as emphasized by the conclusions of the President's National Mathematics Advisory Panel. Recent cognitive, developmental and educational studies have provided new insights into the enduring behavioral deficits in children with mathematical disabilities (MD). However, little is known about the neural and anatomical bases of MD in children. The overarching objective of our proposal is to continue a productive line of research investigating cognitive and brain mechanisms underlying MD in young children. We will use a cognitive and systems neuroscience approach coupled with state-of-the-art functional magnetic resonance imaging (fMRI), structural MRI and diffusion tensor imaging (DTI) techniques to achieve this objective. Our study focuses on ages 7-10 (grades 2, 3 and 4), a period important for mastering core arithmetic skills that support later mathematics learning. A prospective longitudinal design will be used to elucidate the neural correlates of poor arithmetic skills in children with MD and examine why some children with MD have persistent deficits whereas others do not. Our proposed studies focus on three groups of children: (1) children with mathematical learning disabilities (MLD) who have persistent disabilities (low achievement across grades), (2) low achieving but variable (LA-V) children who lag in performance skills in one year and are normal the next, and (3) typically developing (TD) children. We will characterize the behavioral, cognitive and neural profile of information processing deficits during addition and subtraction, two basic and complementary arithmetic operations that differ in task complexity and efficient retrieval. Analysis of DTI and fMRI data acquired from the same children will contribute important new knowledge about core neuroanatomical deficits in persistent MD. Novel multivariate pattern recognition techniques, which detect fine-grained differences in activation patterns, will be used to increase our ability to uncover aberrant neural representations of mathematical information in children with MD. The longitudinal study design will allow us to (1) assess intra- and inter-subject variability and stability of brain response and connectivity in relation to arithmetic skill development, and (2) identify latent classes of neurodevelopmental changes characterizing poor and normal development. Our proposed studies will provide new insights into the neural correlates of MD, and the extent to which increased recruitment of brain networks involved in arithmetic processing during development is altered in children with MD. By providing essential knowledge about the neurofunctional and neuroanatomical substrates of MD in children, and how they change with time, we will be able to inform the development of behavioral and educational strategies for improving mathematical skills at an early age.